Suppose a store owner has 18680000 apples and 68050000 oranges and wants to package them into identical fruit baskets so that every basket contains an equal number of each item without leaving any remainder. What is the maximum number of identical fruit baskets that can be made, and how many of each item will be in each basket?
GCD Problem and Solution:
step 1 Address the method, input parameters and values:
Integers: 18680000, 68050000
Find GCD(18680000 and 68050000) = ?
step 2 Find the prime factors of all integers in the group:
18680000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 467
68050000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 1361
step 3 Identify the common prime factors:
The common prime factors shared by all integers (18680000, 68050000) are: 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5.
step 4 Multiply the common prime factors to find the greatest common factor:
GCD(18680000, 68050000) = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 = 10000.
step 5 Real-world conclusion:
The maximum number of identical fruit baskets that can be made is 10000.
Each basket will contain 1868 apples and 6805 oranges.
GCD(18680000, 68050000) = 10000
